An aeroplane covers 1500 km at a steady speed. Bad weather forces the pilot to fly 100 km/h slower than usual, and the flight then takes 30 minutes longer. Taking the usual speed as x km/h, the situation reduces to x² − 100x − 300000 = 0. Find the usual speed.

Question

Accepted Answer

600 km/h. 1500/x - 100 - 1500/x = 1/2 clears to x² − 100x − 300000 = 0. x = 100 ± √10000 + 12000002 = 100 ± 1100/2 = 600 or −500. The root −500 satisfies the equation but a speed cannot be negative, so it is rejected: the usual speed is 600 km/h. Check: 1500/500 − 1500/600 = 3 − 2.5 = 0.5 hour.

An aeroplane covers 1500 km at a steady speed. Bad weather forces the pilot to fly 100 km/h slower than usual, and the flight then takes 30 minutes longer.
Taking the usual speed as $x$ km/h, the situation reduces to $x^{2} - 100 x - 300000 = 0$ .
Find the usual speed.

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More Class 10 The Quadratic Formula practice

An aeroplane covers 1500 km at a steady speed. Bad weather forces the pilot to fly 100 km/h slower than usual, and the flight then takes 30 minutes longer.Taking the usual speed as x km/h, the situation reduces to x2−100x−300000=0.Find the usual speed.

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 The Quadratic Formula practice

An aeroplane covers 1500 km at a steady speed. Bad weather forces the pilot to fly 100 km/h slower than usual, and the flight then takes 30 minutes longer.
Taking the usual speed as $x$ km/h, the situation reduces to $x^{2} - 100 x - 300000 = 0$ .
Find the usual speed.